Theory of Computation: Counting and Decision Problems

This lecture covers the theory of computation, focusing on counting infinite sets and decision problems. It discusses the concept of countability, demonstrating how to count infinite sets like positive integers and pairs of positive integers. The lecture also explores the notion of decidability, distinguishing between decidable and undecidable problems. It presents examples of decidable problems, such as checking if a number is a multiple of another, and introduces the undecidable halting problem. Through demonstrations of self-reference and paradoxes, the lecture illustrates the limitations of computation in solving certain problems. It concludes by emphasizing the significance of recognizing undecidable problems and the power of self-reference in computational theory.